Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
def b_search(l,r,arr,x) :

    while(l<=r) :
        mid = (l+r)//2

        if x<arr[mid] :
        
            r = mid-1 

        
        elif x>arr[mid] :
        
            l = mid+1 
    
        elif x==arr[mid] :
        
            return True 
        
    return False

n = int(input())

N = math.sqrt(2*n)

arr = []
arr.append(0)

for i in range(1,int(N)+1) :
    
    arr.append(arr[i-1]+i)
    
#print(arr)
    
flag = 1
    
for i in range(1,int(N)) :
    if b_search(0,int(N),arr,n-arr[i]) :
        
        print("YES")
        flag = 0
        break
    
if flag :
    print("NO")